MinT - Best Known (130−50, 130, s)-Nets in Base 5

Best Known (130−50, 130, s)-Nets in Base 5

(130−50, 130, 252)-Net over F₅ — Constructive and digital

Digital (80, 130, 252)-net over F₅, using

10 times m-reduction [i] based on digital (80, 140, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 70, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(130−50, 130, 328)-Net over F₅ — Digital

Digital (80, 130, 328)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(130−50, 130, 10951)-Net in Base 5 — Upper bound on s

There is no (80, 130, 10952)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7 349476 900354 953047 433989 050348 883123 809657 723139 217521 772652 019600 452362 616703 086175 464737 > 5¹³⁰ [i]